## L = { w x (w^r)* ∣ w , x ∈ ( a + b ) * } is it regular language? [duplicate]

L = { w x (w^r)* ∣ w , x ∈ ( a + b ) * } is it regular language? If so, why?

The notation W^r means the reverse string of W.

## Does $\Sigma ^*$ contain $w^R$ for every $w \in \Sigma ^*$?

For any given alphabet $$\Sigma$$, does $$\Sigma ^*$$ contain $$w^R$$ for every $$w \in \Sigma ^*$$ ?

It may be trivial but I can’t quite think how to show it.

(Not sure under which tag to post it)